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🔗 Law 🔗 English Language

"The exception that proves the rule" (sometimes "the exception proves the rule") is a saying whose meaning is contested. Henry Watson Fowler's Modern English Usage identifies five ways in which the phrase has been used, and each use makes some sort of reference to the role that a particular case or event takes in relation to a more general rule.

Two original meanings of the phrase are usually cited. The first, preferred by Fowler, is that the presence of an exception applying to a specific case establishes ("proves") that a general rule exists. A more explicit phrasing might be "the exception that proves the existence of the rule." Most contemporary uses of the phrase emerge from this origin, although often in a way which is closer to the idea that all rules have their exceptions. The alternative origin given is that the word "prove" is used in the archaic sense of "test". In this sense, the phrase does not mean that an exception demonstrates a rule to be true or to exist, but that it tests the rule, thereby proving its value. There is little evidence of the phrase being used in this second way.

🔗 Professional sound production 🔗 Stagecraft

The Schaffer–Vega diversity system (SVDS) was a wireless guitar system developed in 1975–76, engineered and prototyped by Ken Schaffer in New York City, and manufactured by the Vega Corporation, El Monte, California. A handheld microphone version was introduced in 1977.

The system was the first cordless system to be adopted by major rock acts because it solved technical problems common to earlier wireless systems. The reliable sound and freedom of movement it provided paved the way for bands to tour with large multi-level stages in arenas. Schaffer-Vegas were used in the late 1970s and early 1980s by many rock bands such as Pink Floyd (namely guitarist David Gilmour), the Rolling Stones, AC/DC and Kiss.

🔗 Economics

The iron law of wages is a proposed law of economics that asserts that real wages always tend, in the long run, toward the minimum wage necessary to sustain the life of the worker. The theory was first named by Ferdinand Lassalle in the mid-nineteenth century. Karl Marx and Friedrich Engels attribute the doctrine to Lassalle (notably in Marx's 1875 Critique of the Gotha Program), the idea to Thomas Malthus's An Essay on the Principle of Population, and the terminology to Goethe's "great, eternal iron laws" in Das Göttliche.

It was coined in reference to the views of classical economists such as David Ricardo's Law of rent, and the competing population theory of Thomas Malthus. It held that the market price of labour would always, or almost always, tend toward the minimum required for the subsistence of the labourers, reducing as the working population increased and vice versa. Ricardo believed that happened only under particular conditions.

🔗 United States 🔗 Espionage 🔗 Law Enforcement

LOVEINT is the practice of intelligence service employees making use of their extensive monitoring capabilities to spy on their love interest or spouse. The term was coined in resemblance to intelligence terminology such as SIGINT, COMINT or HUMINT.

🔗 Medicine 🔗 Psychology

Posttraumatic Embitterment Disorder (PTED) is defined as a pathological reaction to a negative life event, which those affected experienced as a grave insult, humiliation, betrayal, or injustice. Prevalent emotions of PTED are embitterment, anger, fury, and hatred, especially against the triggering stressor, often accompanied by fantasies of revenge. The disorder commences immediately and without time delay at the moment of the triggering event. If left untreated, the prognosis of PTED presents as rather unfavorable, since patients find themselves trapped in a vicious circle of strong negative emotions constantly intensifying one another and eventually leading into a self-destructive downward spiral. People affected by PTED are more likely to put fantasies of revenge into action, making them a serious threat to the stressor.

The concept of PTED as a distinct clinical disorder has been first described by the German psychiatrist and psychologist Michael Linden in 2003, who remains its most involved researcher. Even though it has been backed up by empirical research in the past years, it remains disputed as to whether embitterment should be included among psychological disorders. Therefore, PTED currently does not hold its own category in the ICD-10 but is categorized under F43.8 “Other reactions to severe stress”. It cannot be categorized as an adjustment disorder under F43.2, since “ordinary” adjustment disorders normally subside within six months, while PTED is much more likely to become chronical and last for much longer. A condition similar to PTED has already been described by Emil Kraepelin as early as 1915 by the name querulous paranoia as a form of traumatic neuroses, explicitly demarcating it from personality disorders.

🔗 Biography 🔗 Poetry 🔗 United Kingdom

The person from Porlock was an unwelcome visitor to Samuel Taylor Coleridge during his composition of the poem Kubla Khan in 1797. Coleridge claimed to have perceived the entire course of the poem in a dream (possibly an opium-induced haze), but was interrupted by this visitor from Porlock while in the process of writing it. Kubla Khan, only 54 lines long, was never completed. Thus "person from Porlock", "man from Porlock", or just "Porlock" are literary allusions to unwanted intruders who disrupt inspired creativity.

🔗 Computing 🔗 Computing/Software 🔗 Linux

The magic SysRq key is a key combination understood by the Linux kernel, which allows the user to perform various low-level commands regardless of the system's state. It is often used to recover from freezes, or to reboot a computer without corrupting the filesystem. Its effect is similar to the computer's hardware reset button (or power switch) but with many more options and much more control.

This key combination provides access to powerful features for software development and disaster recovery. In this sense, it can be considered a form of escape sequence. Principal among the offered commands are means to forcibly unmount file systems, kill processes, recover keyboard state, and write unwritten data to disk. With respect to these tasks, this feature serves as a tool of last resort.

The magic SysRq key cannot work under certain conditions, such as a kernel panic or a hardware failure preventing the kernel from running properly.

🔗 Death 🔗 Korea 🔗 Skepticism 🔗 Alternative Views 🔗 Korea/Korean popular culture working group

Fan death is a widely held belief in Korean culture, where it is thought that running an electric fan in a closed room with unopened or no windows will prove fatal. Despite no concrete evidence to support the concept, belief in fan death persists to this day in Korea, and also to a lesser extent in Japan and Russia.

🔗 Mathematics 🔗 Statistics 🔗 Systems 🔗 Robotics 🔗 Systems/Control theory

In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, one of the primary developers of its theory.

The Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and dynamically positioned ships. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of robotic motion planning and control and can be used in trajectory optimization. The Kalman filter also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, use of the Kalman filter supports a realistic model for making estimates of the current state of the motor system and issuing updated commands.

The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

Optimality of the Kalman filter assumes that the errors are Gaussian. In the words of Rudolf E. Kálmán: "In summary, the following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Though regardless of Gaussianity, if the process and measurement covariances are known, the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense.

Extensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is a hidden Markov model where the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Also, Kalman filter has been successfully used in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filter.

🔗 Mathematics 🔗 Statistics

Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.

The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes:

${\displaystyle Y_{t}=\int _{0}^{t}H_{s}\,dX_{s},}$

where H is a locally square-integrable process adapted to the filtration generated by X (Revuz & Yor 1999, Chapter IV), which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular t is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval. The main insight is that the integral can be defined as long as the integrand H is adapted, which loosely speaking means that its value at time t can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to t and constructs Riemann sums. Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.

Important results of Itô calculus include the integration by parts formula and Itô's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.

In mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount H_t of the stock at time t. In this situation, the condition that H is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through clairvoyance: buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that H is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums (Revuz & Yor 1999, Chapter IV).